IGNOU MST 3 2026 - Four coins were tossed and number of heads noted. The experiment is re

Question

Four coins were tossed and number of heads noted. The experiment is repeated 200 times. The number of tosses showing 0, 1, 2, 3 and 4 heads were found distributed as under. Fit a binomial distribution to these observed results assuming that the nature of the coins is not known.

Number of Heads	0	1	2	3	4
Number of Tosses	15	35	90	40	20

19 Jan 2026

Answer :

Word Count : 432

We are asked to fit a binomial distribution for four coins tossed 200 times with observed frequencies of heads. Let the probability of getting a head on a single coin be (p). For (n = 4) coins, the binomial probability is [ P(X = k) = \binom{4}{k} p^k (1-p)^{4-k}, \quad k = 0,1,2,3,4. ] The observed frequencies are: 0 → 15, 1 → 35, 2 → 90, 3 → 40, 4 → 20. Total tosses = 200. Step 1: Estimate (p) using the mean. The mean of a binomial distribution is [ \mu = n p. ] The sample

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Number of Heads	0	1	2	3	4
Number of Tosses	15	35	90	40	20

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